Energy-Delay Tradeoff in Ultra-Dense Networks Considering BS Sleeping and Cell Association

Ultra-dense network (UDN) is a promising technology for future wireless networks to meet the explosively increasing wireless traffic demands. Sleeping strategy that switches base station (BS) on/off to reduce the energy consumption of UDN is widely investigated. However, the energy saving of sleeping strategy may come at the cost of increased delay. Hence, energy-delay tradeoff (EDT) which means how much energy can be saved by trading off tolerable delay is an important topic. In this paper, we develop a theoretical framework for EDT considering BS sleeping and cell association in UDNs. Firstly, an M/G/1/N processor sharing vacation queueing is introduced to model small cell considering sleeping strategy and cell association. Mean delay and energy consumption are quantitatively studied based on the queueing model. The general expressions for mean delay and energy consumption are derived. It shows that sacrificing delay will not always bring about energy saving. Then, EDT problem is formulated as a cost minimization problem, and the optimal sleeping time and association radius are investigated to achieve the optimal tradeoff between energy consumption and delay. Since there is no closed-form expression for the optimal sleeping time for arbitrary number of users associating with one small cell, the optimal sleeping time for one and infinite number of users are derived. Simulation results demonstrate that the optimal sleeping time for infinite number of users is a reasonable approximation for arbitrary number when it is more than one.